Dioxin generally refers to the molecule TCDD (2,3,7,8-tetrachlorodibenzo-para-dioxin). It is incredibly toxic to mammals. It has an LD50 of 0.04 mg/kg in mice. For comparison, nicotine has an LD50 of 55 mg/kg. In mice, dioxin is 10,000 times more toxic than cyanide. Cobra venom is about 3 times more toxic than dioxin, but dioxin is 200 times more toxic than rattlesnake venom. I suppose that's enough to give you a reference. I don't have any data on human acute toxicity. Everything I have seen seems to suggest the above numbers are a little misleading in terms of acute human toxicity and TCDD is actually quite a bit less lethal to humans (relatively) although even a small exposure can cause a severe skin disease.

TCDD was found to be a side product in the synthesis of "Agent Orange" during the Viet Nam war and caused a lot of problems, although virtually relationship between this exposure and birth defects has been found in these cases according to a 1974 article.

As if the acute toxicity wasn't enough, there are also a lot of problems with chronic exposure over time, including birth defects and cancer.

Unfortunately for everyone in the world, dioxins are formed by the combustion of organic materials in the presence of chlorides. It is estimated that in the forest in Canada alone, about 130 pounds of dioxins (various isomers) are produced every year. Closer to home, your fireplace produces about 0.4 parts per billion of TCDD.

All in all, it's pretty much impossible to prevent any and all exposure to TCDD, but unless you are working in a chemical plant or something equally hazardous, you'll probably never encounter enough to cause any noticeable health problems.

Yes, it may contain dioxin (or TCDD, this is also another name of this chemical). I strongly recommend that you thoroughly wash all vegetables before consuming. I think this chemical is white. So any white particles on vegetables pose a great danger (it may also be some dust, but don't be relaxed).